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In Theory of Computation, we mostly reviewed the mathematical foundations necessary to understand the upcoming models of computation. I went through them pretty quickly, stopping only to introduce the concept of a language. I reviewed equivalence relations and induction in the context of strings and languages, which is a change from years past (this is my sixth year in a row teaching this course). I think keeping the math review focused on languages will be a big help later on.

In Math 101, I already reported on Tuesday’s activities. We did more in-class groupwork on Thursday. We flipped pennies, balanced pennies, and spun pennies, all with the idea of seeing whether our expectations would be met. Turns out that while flipping pennies gives you the results you might expect (about half and half), balancing a bunch of pennies on edge then banging the table yields a preponderance of heads (anyone? anyone?). Spinning the pennies and letting them settle yielded (for the most part) the opposite result, thought not as dramatically, and even then, one of my groups got the “wrong” result. Oh, well.

We also simulated a little class reunion scenario using playing cards (remembered at the last minute that I needed cards and had to run over to the school bookstore to buy some). I won’t go into the details, but it didn’t go as well as I had hoped. I probably needed to explain it a bit better than the book did.

We ran through a couple of other exercises as a class, all with the purpose of showing that you can’t trust your intuition about a lot of these things.

On Tuesday, we’ll revisit some of the results and start talking about the actual mathematics behind all of this.

I should note that I also suggested to the class that if they had nothing better to do on Friday nights (ha!), they could start tuning in to Numb3rs on CBS. I plan to report on each week’s episode over our class discussion board on WebCT. Last night’s episode was especially appropriate since it was all about card-counting and chance. We’ll see how many of my students watched (and no, I’m not holding my breath).

Previous to this (after my one year of using Martin’s 2nd edition), I had been using Hopcroft, Ullman, and Motwani’s Introduction to Automata Theory, Languages, and Computation, 2nd edition. When I first found out that Hopcroft and Ullman’s classic Automata text had been updated after 22 years, I was excited. I thought the 1st edition (which caused me to fall in love with Automata Theory) would be too difficult for my students, and the 2nd edition promised to be more accessible. Unfortunately, I’ve been disappointed. Thus the switch back to Martin.